Identification of Consistent and Inconsistent Academic Achievement in Grouping Units

PSC 290 - Data Visualization

Marwin Carmo

Background

  • The Spike-and-Slab Mixed-Effects Location Scale model (SS-MELSM) methodology identifies clustering units (students, classrooms, etc.) that exhibit unusual levels of residual variability—such as consistency or inconsistency—in academic achievement.

  • The Posterior Inclusion Probability (PIP), quantifies the probability that a given random effect is included in the residual variance (scale) model.

  • Evidence for retaining the random effect is evidence of unusual variability.

Background

  • ivd is a package that facilitates the implementation of the SS-MELSM.

  • Once (in)consistent schools are identified, researchers may want to investigate these clusters to understand what distinguishes them from others.

Research question

How can we visualize these clusters to clearly highlight what makes them unique compared to others?

  • The final goal is to enhance the visualizations currently provided by the ivd package.

Method

  • Standardized math scores from 11,386 11th and 12th-grade students across 160 schools.

  • I will work with posterior estimates from the scale model.

  • Specifically, I will use the PIPs, the estimated random effects standard deviations, the within-school residual variance, and the estimated math scores.

Improvements to existing plots

PIP plot

Old version

New version

Improvements to existing plots

Funnel plot

Old version

New version

Improvements to existing plots

Outcome plot

Old version

New version

New plots

Sugarloaf plots